What is writing?

Writing is a method of representing language in visual or tactile form.
Writing systems use sets of symbols to represent the sounds of speech,
and may also have symbols for such things as punctuation and numerals.

Definitions of writing systems

Here are a number of ways to define writing systems:

a system of more or less permanent marks used to
represent an utterance in such a way that it can be recovered more
or less exactly without the intervention of the utterer.

a set of visible or tactile signs used to represent units
of language in a systematic way, with the purpose of recording messages
which can be retrieved by everyone who knows the language in question and
the rules by virtue of which its units are encoded in the writing
system.

All writing systems use visible signs with the exception of the raised
notation systems used by blind and visually impaired people, such as
Braille and Moon.
Hence the need to include tactile signs in the above definition.

In A History of Writing, Steven Roger Fischer
argues that no one definition of writing can cover all the writing systems
that exist and have ever existed. Instead he states that a 'complete
writing' system should fulfill all the following criteria:

it must have as its purpose communication;

it must consist of artificial graphic marks on a durable or electronic surface;

it must use marks that relate conventionally to articulate
speech (the systematic arrangement of significant vocal sounds) or
electronic programing in such a way that communication is achieved.

Writing systems are both functional, providing a visual way to represent
language, and also symbolic, in that they represent cultures and peoples.
In The writing systems of the world, Florian Coulmas describes
them as follows:

As the most visible items of a language, scripts and orthographies
are 'emotionally loaded', indicating as they do group loyalties and identities.
Rather than being mere instruments of a practical nature, they are symbolic
systems of great social significance which may, moreover, have profound
effect on the social structure of a speech community.